09 Differentiation

15 Feb 2018

Taking numerical derivatives is based on the elementary definition

$$\frac{dy(t)}{dt} := \lim_{h\rightarrow 0} \frac{y(t+h) - y(t)}{h}$$

We will then derive different finite difference approximations to the derivative and assess their error.

Class material

You can follow the lecture in the slides 09-differentiation.ipynb. ¹

For the problem that you should solve during the class, get the notebook 09-differentiation-students.ipynb.²

Additional resources

• Computational Physics: Ch 5.1 – 5.6
• If you are interested in integration then see the lectures on integration in 2016; this year we are skipping this part in favor of more in-depth programming exercises.

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Footnotes